Some meshes follow the armature and some don't
This rigging seems messy, probably because it comes from a game that has its own system, so it would take too long to fix it all, but a quick fix for the hat for example: Go in Edit mode, select all the vertices, go in the Properties panel &gt; Object Data &gt; Vertex Groups, change the name of Root to Root.001, which is the name of the bone that is supposed to control it, then click Assign.